Question

question 7
for the following exercise, determine the interval(s) on which the function in increasing and decreasing. enter \dne\ if the function is never increasing or decreasing.
$f(x) = 4(x + 1)^2 + 7$
increasing:
decreasing:
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Explanation:

Step1: Identify function type

This is a quadratic function $f(x)=4(x+1)^2+7$, which opens upward (since the coefficient of the squared term $4>0$), with vertex at $(-1,7)$.

Step2: Find increasing interval

For upward-opening parabolas, the function increases to the right of the vertex.
Interval: $(-1, \infty)$

Step3: Find decreasing interval

For upward-opening parabolas, the function decreases to the left of the vertex.
Interval: $(-\infty, -1)$

Answer:

Increasing: $(-1, \infty)$
Decreasing: $(-\infty, -1)$